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A Conservative and Monotone Characteristic Finite Element Solver for Three-Dimensional Transport and incompressible navier-stokes equations on Unstructured Grids

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Communications in Computational Physics 2022年第1期31卷 224-256页

作者： Bassou Khouya Mofdi El-Amrani Mohammed Seaid International Water Research Institute University Mohammed VI PolytechnicBenguerirMorocco Mathematics and Applications Laboratory FSTAbdelmalek Essaadi UniversityTangierMorocco Department of Engineering University of DurhamSouth RoadDurham DH13LEUK

We propose a mass-conservative and monotonicity-preserving characteristic finite element method for solving three-dimensional transport and incompressiblenavier-stokes equations on unstructured grids. The main idea in the proposed algorithm consists of combining a mass-conservative and monotonicity-preserving modified method of characteristics for the time integration with a mixed finite elementmethod for the space discretization. This class of computational solvers benefits fromthe geometrical flexibility of the finite elements and the strong stability of the modi-fied method of characteristics to accurately solve convection-dominated flows usingtime steps larger than its Eulerian counterparts. In the current study, we implementthree-dimensional limiters to convert the proposed solver to a fully mass-conservativeand essentially monotonicity-preserving method in addition of a low computationalcost. The key idea lies on using quadratic and linear basis functions of the mesh element where the departure point is localized in the interpolation procedures. Theproposed method is applied to well-established problems for transport and incompressible navier-stokes equations in three space dimensions. The numerical resultsillustrate the performance of the proposed solver and support its ability to yield accurate and efficient numerical solutions for three-dimensional convection-dominatedflow problems on unstructured tetrahedral meshes.

关键词： Mass-conservative monotonicity-preserving modified method of characteristics fi-nite element method convection-dominated problems incompressible navier-stokes equations

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Implementation of the Divergence-Free and Pressure-Oscillation-Free Projection Method for Solving the incompressible navier-stokes equations on the Collocated Grids

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Communications in Computational Physics 2007年第4期2卷 746-759页

作者： Yu-Xin Ren Miao’er Liu Hanxin Zhang Department of Engineering Mechanics Tsinghua UniversityBeijing 100084China CNOOC Research Center Beijing 100027China National Key Laboratory for CFD Beijing 100083China.

In this paper,a divergence-free and pressure-oscillation-free projection method for solving the incompressible navier-stokes equations on the non-staggered grid is *** exact discrete projection method is used to compute the velocity field,which ensures the discrete divergence of the velocity field is *** order to eliminate the odd-even decoupling in the pressure field,a filtering procedure is proposed and applied to the pressure *** have shown this filter recovers the grid scale ellipticity in the pressure field and the odd-even decoupling can be removed *** proposed numerical scheme is further verified through numerical experiments.

关键词： incompressible navier-stokes equations projection methods non-staggered grids pressure filtering.

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A Novel Staggered Semi-implicit Space-Time Discontinuous Galerkin Method for the incompressible navier-stokes equations

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Communications on Applied Mathematics and Computation 2021年第4期3卷 607-647页

作者： F.L.Romeo M.Dumbser M.Tavelli Department of Civil Environmental and Mechanical EngineeringUniversity of TrentoVia Mesiano 7738123 TrentoItaly

A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space *** staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral *** this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is *** the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each *** the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous *** other words,the basis functions on the dual mesh arc built by continuous finite elements on the *** choice allows the construction of an efficient,quadrature-free and memory saving *** our coupled space-time pressure correction formulation for the incompressible navier-stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard *** numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.

关键词： incompressible navier-stokes equations Semi-implicit space-time discontinuous Galerkin schemes Staggered unstructured meshes Space-time pressure correction method High-order accuracy in space and time

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A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the incompressible navier-stokes equations

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Communications in Computational Physics 2009年第2期5卷 712-729页

作者： Abdullah Shah Hong Guo Li Yuan LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100080China Department of Mathematics COMSATS Institute of Information TechnologyIslamabadPakistan

This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible navier-stokes equations in generalized curvilinear *** artificial compressibility approach is used,which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be *** convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting,and the viscous terms are approximated by a fourth-order central compact *** solution algorithm used is the Beam-Warming approximate factorization *** solutions to benchmark problems of the steady plane Couette-Poiseuille flow,the liddriven cavity flow,and the constricting channel flow with varying geometry are *** computed results are found in good agreement with established analytical and numerical *** third-order accuracy of the scheme is verified on uniform rectangular meshes.

关键词： Upwind compact difference flux difference splitting incompressible navier-stokes equations artificial compressibility lid-driven cavity flow

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APPLICATION OF A THREE-POINT EXPLICIT COMPACT DIFFERENCE SCHEME TO THE incompressible navier-stokes equations

APPLICATION OF A THREE-POINT EXPLICIT COMPACT DIFFERENCE SCH...

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全球华人水动力学学术会议

作者： LIN Jian-guo XIE Zhi-hua ZHOU Jun-tao College of Environmental Science and Engineering Dalian Maritime University Dalian 116026 China

＜正＞A three-point explicit compact difference scheme with high order of accuracy for solving the unsteady incompressible navier-stokes equations was presented. Numerical solutions are obtained for the model problem of lid-driven cavity flow and are compared with benchmark solutions found in the literature. It is discovered that the proposed three point explicit compact scheme is not only simple to implement and economical to use, but also is effective to obtain high-order accurate solution in coarse grid systems.

关键词： incompressible navier-stokes equations lid-driven cavity flow high order compact scheme explicit finite difference method

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On the Radius of Analyticity of Solutions to 3D navier-stokes System with Initial Data in L^(p)

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Chinese Annals of Mathematics,Series B 2022年第5期43卷 749-772页

作者： Ruilin HU Ping ZHANG Academy of Mathematics&Systems Science the Chinese Academy of SciencesBeijing 100190China Academy of Mathematics&Systems Science and Hua Loo-Keng Key Laboratory of Mathematics the Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Given initial data u0 ∈ L^(p)(R^(3)) for some p in [3,18/5 [,the auhtors first prove that3 D incompressible navier-stokes system has a unique solution μ=μL+v with μL=^(def)e^(t△)μ_(0) and ν∈L^(∞)([0,T];H^(5/2)-^(6/p)∩L^(1)([0,T];H^(9/2-6/p) for some positive time *** they derive an explicit lower bound for the radius of space analyticity of v,which in particular extends the corresponding results in [Chemin,J.-Y.,Gallagher,*** Zhang,P.,On the radius of analyticity of solutions to semi-linear parabolic system,***.,27,2020,1631-1643,Herbst,*** Skibsted,E.,Analyticity estimates for the navier-stokes equations,*** Math.,228,2011,1990-2033] with initial data in H^(s)(R^(3)) for s ∈ [1/2,3/2[.

关键词： incompressible navier-stokes equations Radius of analyticity Littlewood-Paley theory

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Remarks on Sharp Interface Limit for an incompressible navier-stokes and Allen-Cahn Coupled System

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Chinese Annals of Mathematics,Series B 2023年第5期44卷 663-686页

作者： Song JIANG Xiangxiang SU Feng XIE Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China School of Mathematical Sciences CMA-ShanghaiShanghai Jiao Tong UniversityShanghai 200240China

The authors are concerned with the sharp interface limit for an incompressible navier-stokes and Allen-Cahn coupled system in this *** the thickness of the diffuse interfacial zone,which is parameterized by ε,goes to zero,they prove that a solution of the incompressible navier-stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L^(∞)(L^(2))∩L^(2)(H^(1))sense on a uniform time interval independent of the small parameterε.The proof consists of two parts:One is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev *** the careful energy estimates,a spectral estimate of the linearized operator for the incompressible navier-stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error *** convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak.

关键词： Sharp interface limit incompressible navier-stokes equations AllenCahn equation Spectral estimate Energy estimates

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不可压navier-stokes方程迎风格式及后验误差估计

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高等学校计算数学学报 2007年第2期29卷 97-116页

作者：薛运华胡健伟马海南南开大学数学科学学院教育部核心数学与组合数学实验室南开大学数学科学学院教育部核心数学与组合数学实验室天津 300071

1引言不可压navier-stokes方程作为流体力学的基本方程,其数值计算一直是科学与工程计算关心的问题．本文考虑定常问题: -ε△u+(u·▽)u+▽p = f x∈Ω,▽·u=0 x∈Ω, (1) u =0 x∈(?)Ω．这里ε=1／Re是Reynolds数的倒数,u=(u1,u2,…... 详细信息

1引言不可压navier-stokes方程作为流体力学的基本方程,其数值计算一直是科学与工程计算关心的问题．本文考虑定常问题: -ε△u+(u·▽)u+▽p = f x∈Ω,▽·u=0 x∈Ω, (1) u =0 x∈(?)Ω．这里ε=1／Re是Reynolds数的倒数,u=(u1,u2,…,ud)为待求流速场,p是待求压力场,f=(f1,f2,…,fd)是给定的体力．Ωv(?) Rd(d=2,3)是有界区域,且具有分片Lipschitz连续边界(?)Ω．

关键词： incompressible navier-stokes equations upwind scheme a posteriori error estimates.

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ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE navier-stokes equations

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Acta Mathematica Scientia 2005年第4期25卷 715-730页

作者： Ali I.Nesliturk Department of Mathematics Izmir Institute of Technology P.O. Box 35430 Izmir Turkey

This paper considers the Calerkin finite element method for the incompressible navier-stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble （RFB） functions. The stability features of the residual-free bubble functions for the linearized navier-stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements.

关键词： Galerkin finite element method incompressible navier-stokes equations stability

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Effect of Cambering on the Aerodynamic Performance of Heaving Airfoils

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Journal of Bionic Engineering 2009年第4期6卷 398-404,406-407页

作者： Joel E.Guerrero Postdoctoral Research Fellow Department of CivilEnvironmental and Architectural EngineeringUniversity of GenoaVia Montallegro 1Genoa16145Italy

In the present work,a parametric numerical study is conducted in order to assess the effect of airfoil cambering on the aerodynamic performance of rigid heaving *** incompressible navier-stokes equations are solved in their velocity-pressure formulation using a second-order accurate in space and time finite-difference *** tackle the problem of moving boundaries,the governing equations are solved on overlapping structured *** numerical simulations are performed at a Reynolds number of Re=1100 and at different values of Strouhal number and reduced *** results obtained show that the airfoil cambering geometric parameter has a strong influence on the average lift coefficient,while it has a smaller impact on the average thrust coefficient and propulsive efficiency of heaving airfoils.

关键词： heaving airfoils structured overlapping grids incompressible navier-stokes equations airfoil cambering

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